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Tile-based modeling of DNA self-assembly for two graph families with appended paths

Chloe Griffin and Jessica Sorrells

Vol. 16 (2023), No. 1, 69–106

Branched molecules of deoxyribonucleic acid (DNA) can self-assemble into nanostructures through complementary cohesive strand base pairing. The production of DNA nanostructures is valuable in targeted drug delivery and biomolecular computing. With theoretical efficiency of laboratory processes in mind, we use a flexible tile model for DNA assembly. We aim to minimize the number of different types of branched junction molecules necessary to assemble certain target structures. We represent target structures as discrete graphs and branched DNA molecules as vertices with half-edges. We present the minimum numbers of required branched molecule and cohesive-end types under three levels of restrictive conditions for the tadpole and lollipop graph families. These families represent cycle and complete graphs with a path appended via a single cut-vertex. We include three general lemmas regarding such vertex-induced path subgraphs. Through proofs and examples, we demonstrate the challenges that can arise in determining optimal construction strategies.

graph theory, discrete graph, lollipop graphs, tadpole graphs, DNA self-assembly, nanostructures, flexible tile model
Mathematical Subject Classification
Primary: 92E10, 05C90
Received: 10 September 2021
Revised: 14 January 2022
Accepted: 8 March 2022
Published: 14 April 2023

Communicated by Vadim Ponomarenko
Chloe Griffin
Brown University
Providence, RI
United States
Jessica Sorrells
Converse University
Spartanburg, SC
United States